PAC Classification based on PAC Estimates of Label Class Distributions

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect, the better our estimates of the label class distributions, the better the resulting classifier will be. In this paper we make this observation precise by identifying risk bounds of a classifier in terms of the quality of the estimates of the label class distributions. We show how PAC learnability relates to estimates of the distributions that have a PAC guarantee on their $L_1$ distance from the true distribution, and we bound the increase in negative log likelihood risk in terms of PAC bounds on the KL-divergence. We give an inefficient but general-purpose smoothing method for converting an estimated distribution that is good under the $L_1$ metric into a distribution that is good under the KL-divergence.Comment: 14 page

Stable subnorms revisited

Let A be a finite-dimensional, power-associative algebra over a field F, either R or C, and let S, a subset of A, be closed under scalar multiplication. A real-valued function f defined on S, shall be called a subnorm if f(a) > 0 for all 0 not equal a is an element of S, and f(alpha a) = |alpha| f(a) for all a is an element of S and alpha is an element of F. If in addition, S is closed under raising to powers, then a subnorm f shall be called stable if there exists a constant sigma > 0 so that f(a(m)) less than or equal to sigma f(a)(m) for all a is an element of S and m = 1, 2, 3.... The purpose of this paper is to provide an updated account of our study of stable subnorms on subsets of finite-dimensional, power-associative algebras over F. Our goal is to review and extend several of our results in two previous papers, dealing mostly with continuous subnorms on closed sets

A modeling analysis program for the JPL Table Mountain Io sodium cloud data

Progress and achievements in the second year are discussed in three main areas: (1) data quality review of the 1981 Region B/C images; (2) data processing activities; and (3) modeling activities. The data quality review revealed that almost all 1981 Region B/C images are of sufficient quality to be valuable in the analyses of the JPL data set. In the second area, the major milestone reached was the successful development and application of complex image-processing software required to render the original image data suitable for modeling analysis studies. In the third area, the lifetime description of sodium atoms in the planet magnetosphere was improved in the model to include the offset dipole nature of the magnetic field as well as an east-west electric field. These improvements are important in properly representing the basic morphology as well as the east-west asymmetries of the sodium cloud

Establishing Credibility: Evolving Perceptions of the European Central Bank

The credibility of a central bank’s anti-inflation stance, a key determinant of its success, may reflect institutional structure or, more dynamically, the history of policy decisions. The first years of the European Central Bank (ECB) provide a natural experiment for considering whether, and how, central bank credibility evolves. In this paper, we present a model demonstrating how the high-frequency response of asset prices to news reflects market perceptions of the anti-inflation stance of a central bank. Empirical tests of this model on high frequency data, regressing both the change in the slope of the German yield curve and the change in the euro/dollar exchange rate on the surprise component of price news, suggest significant instability in the market’s perception of the policy stance of the ECB during its first five years of operation. Estimated smoothed paths of the coefficients linking news to asset prices show that these coefficients change with policies undertaken by the ECB. In contrast, there is no evidence of parameter instability for the response of the slope of the United States yield curve to price news during this period, suggesting no comparable evolution in the market perceptions of the commitment to inflation fighting by the Federal Reserve.Central Banking, European Central Bank, Federal Reserve, inflation, exchange rate, credibility, yield curve

A modeling analysis program for the JPL table mountain Io sodium cloud

Progress and achievements in the first year are discussed in three main areas: (1) review and assessment of the massive JPL Table Mountain Io sodium cloud data set, (2) formulation and execution of a plan to perform further processing of this data set, and (3) initiation of modeling activities. The complete 1976-79 and 1981 data sets are reviewed. Particular emphasis is placed on the superior 1981 Region B/C images which provide a rich base of information for studying the structure and escape of gases from Io as well as possible east-west and magnetic longitudinal asymmetries in the plasma torus. A data processing plan is developed and is undertaken by the Multimission Image Processing Laboratory of JPL for the purpose of providing a more refined and complete data set for our modeling studies in the second year. Modeling priorities are formulated and initial progress in achieving these goals is reported

A modeling analysis program for the JPL table mountain Io sodium cloud

A data quality review for the entire set of the 1981 Region B/C images has been completed and is presented. The review indicates that almost all images are of sufficient quality to be valuable in our analysis of this data set. Five data-correlation studies for the same data set have also been completed and are useful in classifying and studying the sodium cloud morphology and its interactions with solar radiation pressure and the plasma torus. Additional progress in developing new image processing techniques and in improving the Io sodium cloud model is also discussed

A modeling analysis program for the JPL Table Mountain Io sodium cloud data

The abundant Io sodium cloud data obtained at JPL Table Mountain was reviewed. Images of the sodium cloud important to this modeling analysis program are contained in the 1976-1979 data set and the 1981 data set. A preliminary assessment of the 263 images in the 1981 data set for Region B/C was initiated. The spatial morphology of some of these images revealed the presence of the forward sodium cloud (Region B) and the directional features (Region C) as expected. Plans for the second quarter to initiate preliminary modeling analysis and to define further data processing are discussed